Jazz, being based on improvisation, was for them a synonym of freedom, which is not what was needed for an authoritarian regime. As a result, all three dictators prohibited jazz and other western music in their countries.
The favorite composers of Hitler were Ludwig van Beethoven, Richard Wagner, and Anton Bruckner. Their powerful, heroic, and especially marshal pieces were inspiring the dictator and, finally, he promoted the three composers as examples of great artists of Nazi Germany. As a result, it came out that Hitler was supporting the German musical tradition, but suppressed creativity – everything was to be close to the set standards.
The situation in the Soviet Union was quite similar. However, the emphasis of Stalin was not on classical music, but on ‘soviet’ music instead. Composers and songwriters were to write only ‘politically correct’ compositions that supported the ideology of the USSR. Most of those willing to create freely did not survive the regime.